All of the 3rd grade teachers and students from Almond went on a field trip to an art museum. Tickets were $$8.00$ each for teachers and $$4.50$ each for students, and the group paid $$68.00$ in total. The next month, the same group visited a science museum where the tickets cost $$16.00$ each for teachers and $$10.50$ each for students, and the group paid $$148.00$ in total. Find the number of teachers and students on the field trips.
Answer: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${8x+4.5y = 68}$ ${16x+10.5y = 148}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-2$ ${-16x-9y = -136}$ ${16x+10.5y = 148}$ Add the top and bottom equations together. $ 1.5y = 12 $ $ y = \dfrac{12}{1.5}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $ {8x+4.5y = 68}$ to find $x$ ${8x + 4.5}{(8)}{= 68}$ $8x+36 = 68$ $8x = 32$ $x = \dfrac{32}{8}$ ${x = 4}$ You can also plug ${y = 8}$ into $ {16x+10.5y = 148}$ and get the same answer for $x$ ${16x + 10.5}{(8)}{= 148}$ ${x = 4}$ There were $4$ teachers and $8$ students on the field trips.